Quitting Smoking: Hypnosis One program to help people stop...

Quitting Smoking: Hypnosis One program to help people stop smoking cigarettes uses the method of posthypnotic suggestion to remind subjects to avoid smoking. A random sample of 18 subjects agreed to test the program. All subjects counted the number of cigarettes they usually smoke a day; then they counted the number of cigarettes smoked the day after hypnosis. (Note: It usually takes several weeks for a subject to stop smoking completely, and the method does not work for everyone.) The results follow. Using a $1 \%$ level of significance, test the claim that the number of cigarettes smoked per day was less after hypnosis.

Quitting Smoking: Hypnosis One program to help people stop smoking cigarettes uses the method of posthypnotic suggestion to remind subjects to avoid smoking. A random sample of 18 subjects agreed to test the program. All subjects counted the number of cigarettes they usually smoke a day; then they counted the number of cigarettes smoked the day after hypnosis. (Note: It usually takes several weeks for a subject to stop smoking completely, and the method does not work for everyone.) The results follow.
Using a $1 \%$ level of significance, test the claim that the number of cigarettes smoked per day was less after hypnosis.

Key Concepts

Paired t-test

The paired t-test is a statistical procedure used to compare the means of two related groups. It evaluates whether the average difference between paired observations is significantly different from zero, accounting for the fact that the data are not independent but are collected from the same subjects under two different conditions.

Significance Level

The significance level, often denoted by ?, is a threshold used in hypothesis testing to decide whether to reject the null hypothesis. It represents the probability of committing a Type I error, which is rejecting a true null hypothesis. A lower significance level, such as 1%, requires stronger evidence from the data to reject the null hypothesis.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. It involves setting up a null hypothesis (typically stating no effect or no difference) and an alternative hypothesis (indicating the presence of an effect or difference), and then using sample data to decide whether to reject the null hypothesis in favour of the alternative.

Paired Sample Design

A paired sample design is used when the same subjects are measured under two different conditions or at two different times, leading to paired (or dependent) observations. This design controls for individual differences among subjects, allowing a more direct comparison of the two conditions by examining the differences within each subject.

One-tailed Test

A one-tailed test is used when the research hypothesis predicts a specific direction of the effect (for example, that one measure is less than the other). In a one-tailed test, the entire rejection region of the test statistic is placed in one tail of the distribution, allowing the researcher to test for an effect in only one specified direction.

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